The use of mathematics in economics and its eﬀect on a scholar’s academic career

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Munich Personal RePEc Archive

The use of mathematics in economics and its effect on a scholar’s academic career

Espinosa, Miguel and Rondon, Carlos and Romero, Mauricio

London School of Economics, International Monetary Fund, University of California San Diego

September 2012

Online at https://mpra.ub.uni-muenchen.de/41363/

MPRA Paper No. 41363, posted 16 Sep 2012 09:13 UTC

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The use of Mathematics in Economics and its Effect on a Scholar’s Academic Career

^∗

(Preliminary version. Comments are welcome.)

Miguel Espinosa^† Carlos Rondon^‡, and Mauricio Romero^§

September 15, 2012

Abstract

There has been so much debate on the increasing use of formal mathematical methods in Eco- nomics. Although there are some studies tackling these issues, those use either a little amount of papers, a small amount of scholars or cover a short period of time. We try to overcome these challenges constructing a database characterizing the main socio-demographic and academic output of a survey of 438 scholars divided into three groups: Economics Nobel Prize winners; scholars awarded with at least one of six prestigious recognitions in Economics; and academic faculty randomly selected from the top twenty Economics departments worldwide. Our results provide concrete measures of mathematization in Economics by giving statistical evidence on the increasing trend of number of equations and econometric outputs per article. We also show that for each of these variables there have been four structural breaks and three of them have been increasing ones. Fur- thermore, we found that the training and use of mathematics has a positive correlation with the probability of winning a Nobel Prize in certain cases. It also appears that being an empirical researcher as measured by the average number of econometrics outputs per paper has a negative correlation with someone’s academic career success.

Keywords: Nobel Prize, Mathematics, Economics, Reputation.

JEL classification numbers: B3, C14, C82, N01

All our mathematics is constructed. It is a construction we make in order to think about the world... [It] is the only way we have to think logically about things we observe...The book of Nature is not written in mathematics; rather, mathematics is the only language we know to explain nature logically.

Ingrid Daubechies

When you have mastered numbers, you will in fact no longer be reading numbers, any more than you read words when reading books. You will be reading meanings.

W. E. B. Du Bois

∗We acknowledge the participation of Laura Cepeda and several other individuals who were extremely helpful in the construction of our data base. We are also indebted to Carlos Alvarez, Raquel Bernal, Javier Birchenall, Juan C.

Cardenas, Jose F. Cata˜no, Nicolas de Roux, Leopoldo Fergusson, Andres Fernandez, Manuel Fernandez, Simon Lodato, Simon Loerschter, Jimena Hurtado, Martin Moreno, Ximena Pena, Jorge Perez, Juan D. Prada, Johanna Ramos, Pascual Restrepo, Tomas Rodriguez, Santiago Saavedra, Glen Weyl, and all the participants of the GIPTE seminar and the Banco de la Republica seminar for their helpful comments. All remaining errors are ours.

†LSE. Ph.D. student,e-mail contact: m.espinosa@lse.ac.uk

‡Research Assistant, International Monetary Fund. e-mail contact: crondon@imf.org

§UCSD. Ph.D. student,e-mail contact: mtromero@ucsd.edu

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1 Introduction

For decades, the increasing use of formal methods in the social sciences has generated controversy. Of these, economics has been the primary focus of criticism. More specifically, most of the debate has centered on the so-called mathematization of economic theory, and the related bias towards formal methods.¹ The central question concerns how the use of mathematics has changed over time in economics, and how its use affects a scholar’s academic career. For our analysis, a database made up of 438 scholars divided into three groups was constructed. The first group consists of 64 individuals that have won the Nobel Prize in economics; the second one consists of 205 individuals selected on the basis of them winning at least one of the following awards: the John Bates Clark Medal (JBCM); Dis- tinguished Fellowship of the American Economic Association (DF); Richard T. Ely Lecturer (RTEL);

Foreign Honorary Member of the American Economic Association (FHM); President of the American Economic Association (PAEA); and President of the Econometric Society (PES)²; the third group consists of 169 scholars randomly selected from the academic faculty of the top twenty economics departments according to IDEAS/RePEc ranking for 2010. For the third group, selection was restricted to academics who had achieved at least an ‘associate professor’ position. These groups are labeled as Nobel Laureates, Awarded Scholars, and Non-Awarded Scholars respectively.

For these authors, all the articles available in JSTOR³ were compiled and reviewed. In order to assess the relative importance of mathematics to their work, we counted the number of equations per article, the number of equations per footnote, the number of econometric results and the number of mathematical appendixes per paper⁴. Although similar methods have been used before, this paper uses a database, that combines an objective measure of each academic’s proximity to mathematics (the average number of equations per paper, a B.A. and/or Ph.D. in mathematics, among others variables) with socio-demographic information (such as country and date of birth, gender, and other related control variables). However, the database lacks a variable for measuring a scholar’s ability or intelligence (e.g., IQ, GRE scores, SAT scores, etc.). Since it is possible that the use of mathematics is correlated with this variable, the econometric models in this article only imply correlation, and by no means causality.

As a general result, the use of mathematics is related with a higher probability of winning a Nobel Prize if the scholar has already won another award, otherwise it reduces the probability of winning any award. Being an awarded scholar is interpreted here as a person who has both a deep understanding

1It has been noted that leading universities and the students themselves regard mathematical knowledge as fundamental to the study of economics. In a survey conducted among graduate students at six leading universities in the U.S., Colander & Klamer (1987) reported that only 3% of students find a thorough knowledge of economic theory as being very important for professional success, compared to 57% who considered excellence in mathematics as fundamental. However, Colander (2005) finds a change in this tendency in recent data, where 9% the students consider a thorough knowledge of economic theory as being very important for professional success, while only 30% considered excellence in mathematics as fundamental.

2The database includes information for the following years: JBCM (1947-2009), DF (1965-2009), RTEL (1962-2009), FHM (1975-2007), PAEA (1930-2010), and PES (1931-2010). Further information can be found in Appendix A.

3Although there are other databases like ECONLIT that specialize in economics, three arguments make JSTOR the most convenient database for the purpose of this article: 1. JSTOR contains articles written before 1900, giving access to the academic production of the oldest scholars; 2. JSTOR also contains journals dedicated to other sciences and areas of knowledge outside of economics; and 3. JSTOR contains journals that have been discontinued or which were completely absorbed by other publications.

4For this article, an equation is defined as any expression that has either variables or numbers, or both, on both sides, such as: x0 =x1,z0> z1 ,w⊂W andp= 1. We consider an econometric result as any econometric output in the form of a table, but, not in the form of a graph. Charts are not included because, our intention is to measure the effect when using a strictly formal mathematical language, although a graph is a functional construction and a mathematical tool in the strict sense of the term. The choice between writing an equation and using a graph has a substantially different effect on the measurement of the so-called “mathematization” of economics. A mathematical appendix is one where a theorem is explained, demonstrated or expanded. Data appendices were not taken into account, since they do not represent expressions in mathematical terms.

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of economic theory and ideas that are socially accepted as brilliant contributions to the state of the art in the mainstream economics. Since mathematics is a natural language for scientific diffusion in economics, we suggest the following explanation: the probability of winning a Nobel Prize rises when brilliant ideas are communicated through a language that other academics understand, and therefore, are easy to disseminate. These results are in line with a vision wherein formality and rigor should be accompanied by a solid understanding of economic theory. This conclusion is robust for different econometric analysis.

Using this database, an analysis of the evolution of mathematics in economics can also be portrayed.

We show that the use of equations per article and the average number of econometric outputs increased consistently over time. Our evidence suggests that the 1950s were a decade of great influence for the way modern theoretical and empirical economics is done. This result is aligned with Debreu (1991) hypothesis wherein he states that during the period 1944-1977, there was a significant increase in the number of pages published in journals related to mathematical economics.

This article contributes to the economics literature in at least four different ways. First, to the best of the authors’ knowledge, a work such as this one has never been done. We are not aware of any article in the literature, which addresses these questions and answers them in the way this article does. Second, the database presented here fills a gap in the literature relating to socio-demographic and academic production in economics. This database has a great potential to test several hypotheses about what economists do and the role of mathematics in the history of the economic thought. Furthermore, conclusions based on this database are a good proxy of what has been happening in the mainstream of economics. Third, we construct an outline of the mathematization of economics in the 20th century, measuring the evolution over time of the average number of equations per article and the average number of econometric outputs per article. Fourth, discrete choice models are presented in order to estimate a scholar’s probability of winning a Nobel Prize and other prestigious awards controlling by different socio-demographic characteristics and several features of his (or her) published articles.

This paper is organized as follows: the next section presents an analysis of the use of mathematics over time, and disentangles certain facts regarding the historic trend. Section 3 presents descriptive statistics of our sample, analyzing such things as geographical origins and scholars’ academic formation.

Section 4 presents our econometric analysis and the results. Section 5 concludes.

2 Mathematics in Economics Over Time

The debate concerning the role of mathematics in economics has been an ongoing one for several years.

A large number of authors, both economists and non-economists, have addressed the subject and have given pros and cons of the intensive use of mathematical methods in studying social problems.

Regardless of this discussion, the incidence of mathematics being utilized in economics has undoubtedly increased, and nowadays an advanced knowledge in mathematics is a basic need for any economist willing to go beyond the undergraduate level. Although there are many arguments both in favor and against the use of mathematics in economics, this article takes no sides whatsoever. The results found here merely attempt to provide an objective account of the use of mathematics in economics through history and the effect this has had on a scholar academic careers⁵.

5According to (Rader 1972), mathematics has at least three important roles in economic theory. First, the production of mathematics is in part an accumulation from other sciences. Second, mathematics is a valuable aid in long sequences of reasoning, where it is easy to make mistakes. Third, mathematics makes possible a greater degree of generality than verbal or graphical methods of discourse. Nevertheless, there are economists who object to the use of mathematics; According to Rader their objections may be summarized in three statements: 1. Mathematical treatment implies quantification, which is impossible for the whole of economics since some variables are not measurable or observable; 2. The search for mathematic generality is a tedious enterprise that substitutes convoluted definitions and notation manipulation for new ideas; and 3. A common question about the use of mathematics in economics is that, even where mathematics does apply, the use of given mathematic result can lead to perverse orientations in economic theory, in as much as mathematical

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Grubel & Boland (1986) found an increasing trend in the use of mathematics in the articles published in the American Economic Review from 1950 to 1983, by counting the number of graphs, diagrams and tables of data as well as the number of equations present in each publication. In a similar exercise, Mirkowski (1991) tabulated the number of pages with mathematical discourse (although he does not explicitly state what he considers as constituting mathematical discourse) from 1887 to 1955 for every volume of four economic journals: the Revue D’Economie Politique, Economic Jour- nal,Quarterly Journal of Economics, and Journal of Political Economy. Between 1887 and 1924, the author found that these journals devoted less than 5% of their pages to mathematical discourse. In contrast, after 1925, about 20-25% of the pages were mathematical in nature. Debreu (1986) quantified the number of pages published per year by the five main periodicals treating mathematical economics (Econometrica, Review of Economic Studies, International Economic Review, Journal of Economic Theory, and Journal of Mathematical Economics) and found that 1930 - 1943 marked a period of decline, while 1944-1977 was a period of “exponential” growth during which the number of pages grew at an annual rate of 8.2%. Debreu (1991) shows that for 1940, less than 3% of the pages of volume 30 of the American Economic Review included mathematical expressions, while in 1990, 40% of the pages of its eightieth volume include sophisticated math.

Although the evidence shows an increasing trend in the use of mathematics in economics, the periods analyzed are insufficient to cover the evolution of academic work in economics throughout the twentieth century. Given that the database created for this article collects information from 1894 to 2006 on the number of equations and econometric outputs in each article published by the featured authors, a possible way to analyze the last century is now possible.

The purpose of this section is to analyze how the use of mathematics and the production of empirical results have evolved over time. Using time-series of the average number of equations and the average number of econometric outputs for the period 1894 - 2006, an analysis based on the trend of both series is proposed for the purpose of identifying possible structural changes. Working with the trend is more appropriate, given that it is more sensible to analyze long term changes than short ones, thus silencing the noise created by year-to-year undesired spikes⁶. Given that the number of structural breaks in both series, as well as their relative position in the series, are unknown, Bai & Perron (2003) methodology fits perfectly. Bai (1997) and Bai & Perron (2003) proved that individual structural change tests for a series containing unknown multiple structural breaks increase the probability of being biased towards not rejecting the hypothesis No presence of structural breaks. Briefly explained, Bai-Perron’s (1998) methodology uses a sequential process of minimization that takes every local minimum in the series as critical points for structural breaks.

Figure 1 shows how the average number of equations per article per year (henceforth, equations p.py) has increased over time, passing from an average of 4 equations per article for the decade 1895 - 1905, to an average of 70 equations per article for the decade 1996 - 2006⁷. Figure 2 shows the evolution of econometric outputs per article (henceforth, econometric outputs p.py) through time. A clear increase in the average number of econometric outputs p.py is evident, especially since the 1950’s.

Before 1950, on average, one finds 1 econometric output for every 10 articles revised; after, one finds 12 econometric outputs for every 10 articles. This steep change in the trend might be related with the introduction of personal computers to the academic world. According to Columbia’s University website⁸, the first attemp of a small scientific computer was designed in that university between 1948 and 1954 by John Lentz. The computer was launched by IBM under the reference IBM-610 Auto-Point

theory is developed along lines not relevant to questions of economic interest.

6In order to isolate the trend of each series, we use a Hodrick-Prescott filter. Following Backus & Kehoe (1992), the smoothing parameter is set at 100.

7Since 1980, a u-shaped trend is observed in the average number of equations p.py. Given data limitations we are not able to provide a formal explanation of this behavior.

8http://www.columbia.edu/cu/computinghistory/610.html

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Computer and included a special control panel to create subroutines involving different mathematical functions. Given that first computers were being designed and tested first in universities; and that these reduced significantly the cost and time of processing large datasets and performing complex calculus, it is plausible that the developing of modern of computers allowed a boom in empirical research that involved econometric analysis and simulations.

050100150Mean of Equations per Paper (p. Year)

1900 1920 1940 1960 1980 2000

year

(Mean) Equations per paper (p. Year) Hodrick-Prescott Trend

Figure 1: The use of equations per article per year.

Source: JSTOR. Calculations: authors.

0123Econometric Outputs per article (p. Year)

1900 1920 1940 1960 1980 2000

year

Hodrick-Prescott Trend (Mean) Econometric Outputs per paper (p. Year)

Figure 2: The use of econometric outputs per article per year. Source: JSTOR. Calculations: authors.

As can be seen in Figure 3, four structural changes were identified in the series ofequations p.py. The years corresponding to those points are 1912, 1952, 1974 and 1990. Figure 4 shows that the Bayesian Information Criterion (BIC) curve is consistent with the selection of four structural breakpoints for this series. Two of the breakpoints identifyed are within the period that Debreu (1991) established as a period of significant increase in the number of pages published in journals featuring mathematical economics. On the other hand, three out of four of these changes are positive, meaning that the average equations per article aumented after the break point. These points were 1912, 1952 and 1990.

Structural break in 1974 is negative and represented a decline in the average of equations per article.

The positive changes are aligned with our hyphotesis of an incresing use of mathematics through time;

however, our data does not allow us to explain the negative change in 1974. In order to fully identify the series, we follow the Box-Jenkins methodology and find that this series is an ARIMA(3,1,0) process.

Similarly, the same methodology was applied to the series of econometricoutputs p.py. Figure 5 shows that the series of econometric outputs has four structural changes in 1918, 1951, 1967 and 1983.

This variable could be modelled as an ARIMA (2,2,2) process. Figure 6 shows the BIC curve for the series and its consistency with the choice of four structural break points. Once again, three out of four breakpoints are associated with an increasing average of econometric outputs per paper. The only negative breakpoint is located between the years 1918 and 1951. After 1951, the positive trend resumes and since then, the average number of econometric outputs per article per year has more than doubled. As we said before, this ever increasing trend might be related with the availability of faster and better computers to researchers.

By itself, finding that 3 out of 4 structural changes were positive does not prove that each series had an increasing trend over the years. However, if we combine these results with the increasing levels in the average of equations and econometrics outputs per paper that were observed in Figure 1 and Figure 2, we can clearly provide evidence of the mathematization in Economics.

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Structural Breaks in the Average Number of Equations per Article

Time

Average Number of Equations per Article, per year

1900 1920 1940 1960 1980 2000

020406080

Figure 3: Structural Breaks in the Average Num- ber of Equations per Article.Source: JSTOR.

Calculations: authors.

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0 1 2 3 4 5

550600650700750800850

BIC and Residual Sum of Squares: Equations p.py

Number of breakpoints

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BIC RSS

200040006000800010000

Figure 4: BIC and Residual Sum of Squares:

Equations p.py. Source: JSTOR. Calculations:

authors.

Structural Breaks in the Econometric Outputs per Article

Time

Average Number of Econometric Outputs per Article, per year

1900 1920 1940 1960 1980 2000

0.00.51.01.52.0

Figure 5: Structural Breaks in the Average Num- ber of Econometric Outputs per Article. Source:

JSTOR. Calculations: authors.

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0 1 2 3 4 5

−250−200−150−100−50050

BIC and Residual Sum of Squares

Number of breakpoints

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BIC RSS

0246810

Figure 6: BIC and Residual Sum of Squares:

Econometric Outputs p.py. Source: JSTOR.

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3 Data Analysis

This section describes some of the most important socio-demographic statistics in our sample. Our specific intention is to provide a descriptive analysis of our database in order to justify and explain the inclusion of certain control variables in the econometric model we will use. This analysis is also revealing because it shows several remarkable facts about the scholars included in our sample.

The database compiles some demographic information about the scholars, such as gender, date and country of birth. It also collects information on their academic backgrounds, namely, where they got their B.A, M.A or Ph.D. (both university and country), and what subject of study they chose. We divided the subject of study into economics, mathematics and other. Mathematics includes applied and theoretical mathematics, but not physics or other related subjects.

3.1 Generalities

The average number of papers per author in our database is 18.81; however, there is great variation between authors. For instance, the scholar with the most articles has 126 papers, and the one with the least number of articles has 1 one paper. The average number of pages, footnotes and equations per paper are 17.5, 15.8 and 56.0, respectively. The average number of equations in footnotes is 5.3.

Finally, 0.51 and 1.75 are the average number of mathematical appendices per paper and the average number of econometrics tables per paper, respectively.

As can be seen in the left panel of Figure 7, Non-Awarded Scholars are the younger group, while Awarded Scholars and Nobel Laureate have a similar age distribution. However, if we compare the age when Awarded Scholars and Nobel Laureates received their first prize with the current age of Non-Awarded Scholars, the distribution is very similar (right panel of figure 7). This last comparison is reasonable because Non-Awarded scholars would pass on to another group once they win their first prize. This suggests that Non-Awarded Scholars are more comparable to Nobel Laureates and Awarded Scholars before the scholars in these last two groups won their first prize. Therefore, from now, when is relevant, all exercises will be performed comparing the entire academic production of all three groups up through 2010 and using only the academic production of Nobel Laureates and Awarded Scholars up through the year they won their first prize. In general the conclusions from the statistical exercises do not change if we change the time frame for which the academic production of Nobel Laureates and Awarded Scholars is taken.

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Years since birth up to 2011 by group

Years since birth up to 2011

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Nobel Laureates Awarded Scholars Non−Awarded Scholars

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Age at first prize, or years since birth up to 2011

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Figure 7: Kernel density estimation of year of birth/age per group, with a bandwidth of 5 given by Silverman’s “rule of thumb”. Source: JSTOR. Calculations: authors.

Table 1 shows descriptive statistics for the three different groups in our sample: Nobel Laureates, Awarded Scholars and Non-Awarded Scholars. It also includes information for Nobel Laureates and Awarded Scholars taking into account only their academic production up through the year they won their first prize. Non-Awarded Scholars have, on average, more equations per page, equations in footnotes, mathematical appendices and econometric tables per article than scholars that won any of the awards being considered, either before they win any award or after. Nonetheless, on average, scholars that have not won any award have fewer papers published. That is less production but more mathematical and empirical intensive research for Non-Awarded Scholars. On the other hand, Awarded Scholars do less empirical intensive research after their first award, while both Awarded Scholars and Nobel Laureates use less equations after being awarded.

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Papers Pages per Pa- per

Equations Equations per Footnote

Mathematical Appedixes

Econometric Outputs Nobel Prize Winners (N=64)

Mean (SD) 25.88 (21.02)

15.97 (5.59) 50.12 (52.79) 3.4 (4.34) 0.42 (0.47) 0.52 (1.08)

Min/Max 1/119 9.02/37.33 0/212.38 0/26 0/1.2 0/6.21

Nobel Prize Winners Prior to First Prize Mean (SD) 14.62

(10.82)

15.46 (4.39) 53.58 (57.07) 3.4 (4.34) 0.13 (0.31) 0.44 (0.78)

Min/Max 0/51 7/31.66 0/247.16 0/26 0/2 0/3.85

Awarded Scholars (N=205) Mean (SD) 22.61

(19.17)

15.57 (5.06) 39.01 (61.62) 3.02 (7.13) 0.49 (0.77) 0.86 (1.43)

Min/Max 1/156 0.636/37.38 0/478.31 0/86.27 0/9.09 0/8

Awarded Scholars Prior to First Prize Mean (SD) 16.40

(15.13)

15.55 (6.46) 41.26 (66.46) 3.02 (7.13) 0.16 (0.61) 1.26 (3.06)

Min/Max 0/116 0.67/43 0/478.31 0/86.27 0/7.66 0/25.42

Non-Awarded Scholars (N=169) Mean (SD) 12.2

(10.41)

20.45 (6.63) 78.91 (74.08) 9.03 (29.33) 0.58 (0.64) 2.69 (3.78)

Min/Max 1/52 1.2/45 0/494 0/247 0/4 0/22.4

Table 1: Source: JSTOR. Calculations: authors.

Figure 8 shows a kernel density estimation of the mean number of equations per page for our different groups. As can be seen, the Non-Awarded Scholars distribution has a higher level of skewness.

The distribution does not change drastically whether we use the entire academic production of Nobel Laureates and Awarded Scholars up to the year they won their first prize or up to 2010.

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Using the articles produced up to the year when scholars won their first prize (if any).

Mean number of equations per paper

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Using the articles by Nobel Laureates and Awarded Scholars produced up to 2010.

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Figure 8: Kernel density estimation, with a bandwidth of 4 given by Silverman’s “rule of thumb”, of the mean number of equations per group. Source: JSTOR. Calculations: authors.

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Table 2 shows the mean difference in the use of mathematics for our different groups. Performing a ttest for the difference in means we find that Non-Awarded Scholars use a greater number of equations compared to Nobel Laureates and Awarded Scholars. Using a “proportion test” to find out whether differences in the proportions of scholars above the median (ei) is greater in one group that in another, we find that fewer Awarded Scholars than Nobel Laureates use more equations than the median, but that proportionately more Non-Awarded Scholars are over the median than any other group. For example, on average, Nobel Laureates and Awarded Scholars use 37.261 fewer equations per paper than Non-Awarded Scholars and that proportion of scholars above the median is 0.332 greater for Non-Awarded Scholars than for Nobel Laureates and Awarded Scholars. These results suggest that, on average, Non-Awarded Scholars used more mathematics, but that if we restrict ourselves to Awarded Scholars and Nobel Laureates, the last group uses more equations on average. Table 3 contains similar information but using only the academic production of Nobel Laureates and Awarded Scholars up to and including the year when they won their first prize; the results are similar to those in table 2.

It can be seen from Tables 2 and 3 that the difference in the mean number of equations between groups is in general smaller (except for Nobel vs. Awarded Scholars) when we restrict the articles used for Nobel Laureates and Awarded Scholars to those published before they won their first prize.

However, they are both significant. Interestingly, the third row has the only not significant difference.

Perhaps, the effect of less equations of Awarded Scholars with the effect of more equations from the Non-Awarded Scholars (both with respect to the Nobel Prize Winners) cancel each other out.

Groups Mean difference in the use

of equations

Proportional difference of ei

Nobel vs. Awarded (i=1) 11.111 0.162^∗∗

Nobel vs. Non-Awarded (i=2) −28.794^∗∗∗ −0.175^∗∗

Nobel vs. Awarded + Non-Awarded (i=3) −6.921 −0.037 Awarded vs. Non-Awarded (i=4) −39.905^∗∗∗ −0.351^∗∗∗

Nobel+Awarded vs. Non-Awarded (i=5) −37.261^∗∗∗ −0.332^∗∗∗

*** p<0.01, ** p<0.05, * p<0.1

Table 2: Mean difference in the use of equations by group. Variables measured using the articles by Nobel Laureates and Awarded Scholars produced up to 2010. Source: JSTOR. Calculations: authors.

Groups Mean difference in the use

of equations

Proportional difference of ei

Nobel vs. Awarded 12.318 0.152^∗∗

Nobel vs. Non-Awarded −25.332^∗∗∗ −0.148^∗∗

Nobel vs. Awarded + Non-Awarded −5.406 −0.058

Awarded vs. Non-Awarded −37.650^∗∗∗ −0.346^∗∗∗

Nobel+Awarded vs. Non-Awarded −34.731^∗∗∗ −0.329^∗∗∗

*** p<0.01, ** p<0.05, * p<0.1

Table 3: Mean difference in the use of equations by group. Variables measured using only the academic production of Nobel Laureates and Awarded Scholars up to and including the year when they won their first prize. Source: JSTOR.

According to Table 4 economics is the predominant subject of study chosen for B.A.s and Ph.D.s.

However, there is an important presence of mathematics in the sample. Comparing the subsamples, it is clear that Nobel Prize laureates make up the largest percentage of scholars with a B.A. or a Ph.D. in mathematics. With the exception of Nobel Laureates, almost 70% of scholars have a B.A in economics.

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%B.A %Ph.D.

Economics Math Economics Math Nobel Laureates 39.1% 32.8% 78.1% 12.5%

Awarded Scholars 68.9% 22.3% 85.6% 5.2%

Non-Awarded Scholars 68.8% 17.4% 89.8% 3.7%

Finally, according to the collected information 52% of our sample are born in the U.S.A. , while 16% are U.S.A. nationalized citizens. That is, almost 70% of the scholars in our survey have a U.S.A.

nationality in one or other way.

3.2 Prizes

Table 5 shows the distribution of awards in our sample for Nobel Prize recipients. In order to properly interpret the table, lets consider for instance the first row. PAEA stands for the presidency of the AEA, and the number in parenthesis refers to the number of presidents in our sample. The number of Nobel Prize recipients that were presidents of the AEA after (or the same years) being a Nobel recipient is eight (out of 80 recipients) and there are 14 scholars that were president of the AEA before being elected a Nobel recipient. The fourth column shows that 34.4% of all Nobel winners were president of the AEA as well. The fifth column shows that 27.5% of the presidents of the AEA were Nobel recipients.

Remarkably, the award with the largest percentage of Nobel winners is the PAEA, while the one with the lowest percentage is FHM. As expected, none of the JBCM winners who won a Nobel, won it prior to winning the JBCM, in an as much as the JBCM is restricted to scholars under 40. As an interesting remark, from the sample of Nobel Laureates and Awarded Scholars, 164 scholars (61.19%

of the total) have only won one award.

Award After or S.Y. Before % Nobel % Prize Mean Age

PAEA (80) 8 14 34.4 27.5 61.33

RTEL (47) 2 10 18.8 25.5 61.10

DF(87) 1 16 26.6 19.5 68

FHM (39) 1 4 7.8 12.8 53

JBCM (31) 0 12 18.8 38.7 37.51

PES (71) 12 18 31.3 28.2 49.84

4 The effect of using mathematics

The objective of our econometric analysis is to determine the influence of academic formation in mathematics and the use of mathematics itself over the academic career of a scholar. Several discrete choice models are proposed in order to find which socioeconomic and academic factors are determinants of the probability of being awarded the Nobel Prize or another award.

Before setting up the model, a more general debate must be resolved. When analyzing the incidence of academic formation of and mathematics used by scholars vis-`a-vis the possibility of achieving success and academic recognition, it is necessary to consider the problem of the possible interaction of both sides of this equation with unobservable factors. This problem stems from the existence of a series of

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factors that may influence the election of a Nobel Prize winner or the winner of another prestigious award and which, because of insufficient information, are non-observable such as IQ, ability and the size and quality of a scholar’s social network.

The database lacks a variable measuring a scholar’s ability or intelligence (e.g., IQ, GRE scores, SAT scores, etc.), and since it is possible that the use of mathematics is correlated with this, the econometric models in this article may suffer from endogeneity. We do not have an instrumental variable that helps disentangle the effect of ability over the probability of winning a Nobel Prize. As a result, our empirical findings only imply correlation, and by no means causality. Nevertheless, to complement our results we present explanations assuming that the relationship between the use of mathematics and the probability of winning an award are direct.

Now regarding our model, as variables, mathematical formation and intensive use of mathematics must be approximated, in as much as they are not observable. We believe that B.A. or Ph.D. in mathematics is a proxy of mathematical formation although its not perfect since there are other degrees corresponding to a curriculum with a high concentration in mathematics or individuals who learned mathematics out of personal interest. To measure the use of mathematics, as we explained in the introduction, we use, as a proxy, the average number of equations per paper and per footnote for the articles in our sample. Dummy variables for those who won any of the awards being considered are also included where necessary. This allows for a control for academic success, reputation and to some extent, networking, given the interconnectedness of the prizes; it is possible that winning one of them results in a social referent, that will lead to a nomination for another prize. Variables for gender and year of birth are also included⁹.

Because the main objective is to explain the probability of winning a prestigious award in economics based on proxy variables for the use of mathematics, a Probit model is used¹⁰. The model to be estimated is:

P(Y = 1|X, M) = Φ(βX+γ1M) +ǫ, (1)

where X is a set of controls; M measures the use of mathematics, which can either be the average number of equations used or the dummy variable ei which is equal to one if someone uses more equations than the median of the population under study. The variable γ¹ shows the general effect of using more mathematics on the probability of belonging to group Y (which can be either Nobel Laureates, Awarded Scholars, or both).

Five different exercises were performed, using all the reasonable combinations of treatment and control groups: Nobel Laureates compared to (1) Awarded Scholars, to (2) Non-Awarded Scholars, and to (3) both; (4) Awarded Scholars compared to Non-Awarded Scholars; and (5) Nobel Laureates and Awarded Scholars compared to Non-Awarded Scholars. Exercises were performed measuring academic output variables in two different ways. The first measure uses all the papers written by an author, the second one, which only affects Awarded Scholars and Nobel Laureates, uses only the papers written by an author the year he won his first prize or prior to that year (in the case of Non-Awarded Scholars it uses all their articles). The objective of this second exercises is to compare Awarded Scholars and Nobel Laureates to Non-Awarded Scholars at a point when their academic careers were most similar.

Tables 6-10 show the results. The first two columns in each table include all the academic work up to 2010 of every scholar. The last columns only use the academic work produced the year Nobel Laureates and Awarded Scholars won their first prize or prior to it. The results of all 5 tables are in general similar.

9We tried to use, as proxy of the quality of the education recieved, a dummy variable indicated if the Ph.D. was done at a top ten university according to the IDEAS/RePEc ranking for 2010. We also tried to use, as proxy for networking, a dummy variable indicating whether or not a scholar is or not in the book “Who’s Who in Economics” (Blaug &

Vane 2003). As it turned out, both of these two variables were not significant to several specifications, and therefore were not included in the final exercises.

10All the results hold for different specifications, and can be found in Appendix D.

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In the enconometric tables below, pages is the mean number of pages of all papers written by a scholar; e f oot is the average number of equations per footnote; jbcm d,df d, f hm d and pes d are dummy variables indicating whether a scholar has won the John Bates Clark Medal, has been a Distinguished Fellow, has been a Foreign Honorary Members or has been President of the Econometric Society; age award indicates the age when the scholar won his first awar; age squared is the square of this number; phd math and math are dummy variables for a Ph.D. and an undergraduate degree in mathematics; phd other and other are dummy variables for a Ph.D. and an undergraduate degree in an area other than economics or mathematics; d iare dummy variables for the decade in which the scholar was born (for example d1880 is equal to one if the scholar was born between 1880 and 1889);

se is the mean number of econometrics outputs per paper; pp is the mean number of footnotes per paper; equations is the average number of equations per paper; prize is equal to one if a scholar has won an award different from the Nobel Prize; namy is the mean number of mathematical appendices per paper; ei has the same meaning as in section 3.1 and Table 2. All variables were included in the final exercises unless there were specification problems.

As can be seen in Table 6, which compares Awarded Scholars with Nobel Laureates, more mathematics - measured as equations and e1 - have a positive correlation with the probability of winning a Nobel Prize. A formation in mathematics, measured by math also has a mild positive correlation and this effect is stronger before winning their first prize. The results confirm the general intuition that the JBCM is a good indicator of future Nobel Prizes. Although, it may seem strange to use a dummy variable for awards when the information prior to any of the scholars winning their first prize is used, this variable might be representing non observable characteristics, such as networking. These non observable characteristics are still present before the scholars win their first award. For the sake of completeness, a regression without the variables for the awards was done as well and is presented in the last two columns.

The age at which a scholar was awarded his first prize has a quadratic effect. It seems you need to reach a certain age (or gain a certain level of experience) in order to be eligible for a Nobel Prize, but beyond a certain threshold, it might be too late. Having a Ph.D. in an area other than mathematics or economics has a positive correlation with the probability of winning a Nobel Prize. pages has a positive effect, which can be explained by the fact that there is space restriction in most journals; thus, if one is permitted extend oneself, it should be because one is writing about something worthy. Finally, the number of econometric outputs (se) has a mild negative effect. This result could be interpreted as follows: ceteris paribus, if someone does more empirical intensive research, he or she may be focusing on proving theories rather than proposing them, and it seems academia does not recognize this kind of contribution as much (in award terms) as less empirical intensive contributions. The results from columns 1 and 2 are similar to those in the last columns. The results in the following tables are similar and if not, differences will be pointed out.

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Nobel vs Awarded

(1) (2) (3) (4) (5) (6)

VARIABLES

equations 0.006** 0.007** 0.004*

(0.003) (0.003) (0.002)

e1 0.772** 0.692** 0.830***

(0.317) (0.332) (0.289)

gender -1.770*** -1.452*** -1.810*** -1.519*** -0.858* -0.536

(0.449) (0.462) (0.455) (0.453) (0.498) (0.519)

age award 0.817*** 0.745*** 0.939*** 0.855*** 0.470*** 0.464***

(0.191) (0.183) (0.218) (0.207) (0.131) (0.128)

age square -0.005*** -0.005*** -0.006*** -0.005*** -0.003*** -0.003***

(0.001) (0.001) (0.002) (0.002) (0.001) (0.001)

d 1890 5.585*** 5.487*** 5.621*** 5.603*** 3.843*** 5.153***

(0.649) (0.667) (0.691) (0.707) (0.368) (0.419)

d 1900 5.882*** 5.757*** 5.978*** 5.828*** 3.597*** 4.799***

(0.553) (0.582) (0.582) (0.589) (0.368) (0.442)

d 1910 6.591*** 6.514*** 6.491*** 6.357*** 3.853*** 4.953***

(0.609) (0.629) (0.674) (0.678) (0.274) (0.321)

d 1920 6.143*** 5.867*** 6.030*** 5.770*** 3.631*** 4.517***

(0.557) (0.568) (0.617) (0.651) (0.302) (0.421)

d 1930 6.775*** 6.475*** 6.769*** 6.489*** 3.847*** 4.777***

(0.634) (0.626) (0.710) (0.690) (0.355) (0.432)

d 1940 6.306*** 5.879*** 6.380*** 6.001*** 3.868*** 4.726***

(0.682) (0.735) (0.830) (0.871) (0.404) (0.500)

d 1950 6.559*** 6.216*** 6.394*** 6.150*** 4.452*** 5.298***

(0.750) (0.794) (0.801) (0.849) (0.601) (0.635)

math 0.501 0.574 0.673* 0.743** 0.655** 0.706**

(0.361) (0.351) (0.389) (0.376) (0.305) (0.308)

other 0.419 0.437 0.440 0.466 0.535** 0.555**

(0.319) (0.318) (0.345) (0.341) (0.273) (0.281)

phd math 0.099 -0.052 0.150 0.060 -0.080 -0.174

(0.422) (0.427) (0.444) (0.458) (0.399) (0.416)

phd other 1.196*** 1.222*** 1.235*** 1.226*** 0.831** 0.976**

(0.429) (0.419) (0.462) (0.451) (0.385) (0.390)

namy -1.569* -1.239 -1.224** -0.853 -0.169 -0.171

(0.841) (0.859) (0.540) (0.538) (0.560) (0.538)

se -0.250* -0.313** -0.243 -0.314** -0.150* -0.191**

(0.130) (0.122) (0.155) (0.153) (0.090) (0.097)

pages 0.090*** 0.099*** 0.113*** 0.121*** 0.042 0.048*

(0.033) (0.033) (0.037) (0.036) (0.028) (0.029)

pp -0.020 -0.028 -0.015 -0.020 -0.006 -0.006

(0.019) (0.019) (0.017) (0.017) (0.013) (0.014)

e foot 0.010 0.013 0.008 0.010 -0.001 0.000

(0.014) (0.013) (0.013) (0.013) (0.013) (0.013)

jbcm d 3.257*** 2.916*** 4.218*** 3.674***

(0.613) (0.541) (0.863) (0.811) df d -1.739*** -1.748*** -1.697*** -1.691***

(0.412) (0.412) (0.419) (0.419) fhm d -1.340*** -1.373*** -1.430*** -1.421***

(0.446) (0.424) (0.488) (0.458)

paea d -0.770* -0.737* -0.636 -0.611

(0.395) (0.408) (0.405) (0.409)

rtel d -0.156 -0.090 -0.102 -0.044

(0.409) (0.413) (0.419) (0.418)

pes d 0.300 0.272 0.366 0.406

(0.337) (0.340) (0.365) (0.378)

Constant -38.035*** -35.475*** -43.022*** -39.973*** -22.104*** -23.365***

(6.726) (6.367) (7.869) (7.415) (4.493) (4.256)

Observations 240 240 234 234 234 234

Robust standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

Table 6: The first two columns compare Nobel Laureates and Awarded scholars using their papers from their academic careers up through 2010. The last four columns only feature papers produced the year the scholars won their first prize or prior to it. Source: JSTOR. Calculations: authors.

Table 7 shows that, when comparing Nobel Laureates with Non-Awarded Scholars, there is little evidence that using more mathematics is correlated with winning a Nobel Prize. Conversely,equations and e2 have a mild negative correlation. However, it seems that mathematical formation, measured by math, does have a positive correlation. This suggests that the use of mathematics increases the probability of winning a Nobel Prize only if you are an Awarded Scholar, but that a mathematical formation augments the probability in either case (see Tables 6 and 7). The negative effect of the mean number of econometric outputs per paper persists.

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Nobel Vs Non-Awarded

(1) (2) (3) (4)

VARIABLES

equations -0.006 -0.010*

(0.007) (0.005)

e2 -0.919 -0.874

(0.724) (0.561)

d 1920 -0.346 -0.152 0.463 0.469

(0.667) (0.648) (0.730) (0.702)

d 1930 -0.976 -0.772 -0.397 -0.338

(0.714) (0.779) (0.623) (0.632) d 1940 -1.445** -1.437** -0.838* -0.900*

(0.651) (0.649) (0.478) (0.478) d 1950 -3.053*** -2.915*** -2.356*** -2.363***

(0.790) (0.770) (0.704) (0.685)

math 3.133*** 3.322*** 2.415*** 2.415***

(0.930) (1.004) (0.713) (0.712)

other 0.795 0.695 0.872* 0.727

(0.581) (0.539) (0.496) (0.464)

phd math 0.003 -0.138 0.192 -0.075

(0.633) (0.569) (0.523) (0.549) namy -5.963*** -5.748*** -2.854*** -2.723***

(1.218) (1.204) (0.609) (0.693) se -0.603*** -0.632*** -0.591*** -0.565***

(0.153) (0.163) (0.174) (0.175)

pages -0.005 -0.011 0.003 -0.002

(0.055) (0.053) (0.058) (0.058) pp -0.139*** -0.145*** -0.082*** -0.079***

(0.040) (0.042) (0.031) (0.030) e foot 0.181*** 0.181*** 0.144*** 0.124***

(0.048) (0.049) (0.043) (0.037) Constant 4.318*** 4.512*** 2.785*** 2.695***

(1.042) (1.081) (0.798) (0.781)

Observations 117 117 113 113

Robust standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

Table 7: The first two columns compare Nobel Laureates and Non-Awarded scholars based on papers from their entire academic careers up through 2010. The last two columns reference only papers by Nobel Laureates produced the year they won their first prize or prior to it. Source: JSTOR. Calculations: authors.

Table 8 shows the results when comparing Nobel Laureates with everyone else (Awarded and Non- Awarded Scholars). The variable prize is a dummy variable equal to one if the scholar won any of the seven awards apart from the Nobel Prize. Let interaction be equal to prize∗equations and interaction2 = prize∗e3. Mathematics have a mild negative effect when measured using e3, but a positive effect for award winners. From these results, as well as those found in Tables 6 and 7, it seems that a greater use of mathematics leads to a higher probability of success in academia only if you are an award winner.

The effect of the variable P rize is negative, which might be explained by the fact that most of the award winners do not go on to become Nobel Laureates. Note that the number of mathematical appendixes is not significant for columns 3 and 4.